Membrane distillation is a process for the evaporation and subsequent condensation of volatiles from a solution via a membrane. In membrane distillation two liquids interface on opposite sides of an hydrophobic (non-wettable) membrane such as polyvinylidine difluoride (PVDF), polytetrafluoro ethylene (teflon) or polypropylene. The driving force of membrane distillation is the vapour pressure gradient resulting from the temperature difference between the two solutions (i.e., between the two surfaces of the membrane). Water evaporates at the solution-membrane interface on the higher temperature side of the membrane and is transported across the membrane to the cooler side thereof. Depending on the application the water vapour pressure is either condensed or discarded on reaching the cool side of the membrane. Heat must be continually supplied to the evaporating surface to provide the latent heat of vaporisation. The converse applies at the condensing surface.
As indicated above the driving force for membrane distillation is the difference in vapour pressure resulting from the two solutions at different temperatures. The difference in vapour pressure is given by the Antoine equation: ##EQU1## where .lambda.=water vapour pressure (mm Hg)
T=liquid temperature (.degree.C.). PA0 r=membrane pore radius (m) PA0 .epsilon.=membrane porosity (o) PA0 R=universal gas constant (J/mol/K) PA0 T=average temperature (K.) PA0 M=vapour molecular weight (kg/g.mol) PA0 .DELTA.P=trans-membrane pressure drop (Pa) PA0 l=membrane pore length (m). PA0 P.sub.1, Po=vapour pressure distalland and distallate, and wherein PA0 N, r, R and T retain their previous definitions. PA0 the shear rate on both sides; PA0 the conductibility coefficient of the membrane.
In cases where the membrane pore size is less than the mean free molecular path of the permeating molecules, it is reasonable to assume that the molecules collide more frequently with the pore walls than they do with each other. This is referred to as the Knudsen flow system wherein the equation for vapour flux is given as: ##EQU2## where N=vapour flux (g.mol/m.sup.2 /s)
The vapour flux across the membrane is inversely proportional to the membrane thickness and thus the use of thinner membranes is beneficial. However, the heat exchanging properties and therefore the effective temperature gradients across the membrane vary with thickness. There are two types of heat flow through the membrane which have to be taken into consideration, namely:
(i) Q.sub.C being the heat flow (Kjoule/m.sup.2 /sec) associated with evaporation of the solvent from one side of the membrane and condensation on the other; and
(ii) Q.sub.L being the heat flow due to losses through the membrane acting as a heat exchanger.
Thermal efficiency of the membrane can be expressed as: ##EQU3##
Q.sub.C is proportional to N and is inversely proportional to "l"
Q.sub.L is also inversely proportional to "l".
In the case of Knudsen flux distillation the efficiency is independent of the thickness of the membrane for a given wall temperature difference EQU .DELTA.Tw=T.sub.2w -T.sub.1w (see FIG. 2, below).
In cases where the membrane pore size is much greater than the mean free path of the permeating molecules, the molecules collide more frequently with each other than they do with the pore walls, and the transfer phenomena is different. This is referred to as the Poiseuille flow system and is based on the theory of viscous flow, where the pressure drop accompanying flow arises from the shear stresses within the fluid. The equation for vapour flux by Poiseuille flow is given by ##EQU4## where .eta.=vapour viscosity
The membrane characteristic Cp is again a function of the membrane geometry. ##EQU5##
Again the efficiency is independent of thickness of the membrane for a given wall temperature difference.
In both cases the vapour flux N is therefore dependent of a given membrane material and structure, only of T.sub.2 w-T.sub.1 w) these values being related to T.sub.1 and T.sub.2 by
In both cases a reduction in thickness will increase the conductibility coefficient accordingly therefore reducing the relative value of .DELTA.Tw when compared with .DELTA.T=T.sub.2 -T.sub.1.
For this reason, membrane distillation is a process where a trade off is necessary when choosing the membrane thickness between the non-acceptable heat losses associated with thin membranes and the non-acceptable low flux associated with the low membrane coefficient of thick membranes.